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General Form of an Update Operator

Prerequisites

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Description

A dynamical system's formalization involves time evolution of the system state under an update rule. This rule generally maps valid system states onto other valid system states.

Equation

\[\htmlId{tooltip-updateOperator}{T} : \htmlId{tooltip-stateSpace}{\mathcal{X}} \rightarrow \htmlId{tooltip-stateSpace}{\mathcal{X}}\]

Symbols Used

\(T\)

This is the symbol for a dynamical system's update operator.
\(\mathcal{X}\)

This symbol represents all possible states of a dynamical system.

Example

Examples of update operator formulations:

  1. Discrete Time Update Operator
  2. Stochastic Discrete Time Update Operator

References

  1. Jaeger, H. (n.d.). Neural Networks (AI) (WBAI028-05) Lecture Notes BSc program in Artificial Intelligence. Retrieved May 17, 2024, from https://www.ai.rug.nl/minds/uploads/LN_NN_RUG.pdf

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